BELOW IS THE DISCUSSION QUESTION AND BELOW IT IS THE DATA CREATED IN MINI TAB TO
ID: 3331661 • Letter: B
Question
BELOW IS THE DISCUSSION QUESTION AND BELOW IT IS THE DATA CREATED IN MINI TAB TO HELP ANSWER THE QUESTION. OCCURRENCES ARE MARKED WITH SIGNS, BUT PLEASE CHECK OVER TO MAKE SURE ALL ARE MARKED. PLEASE DO YOURE BEST TO ANSWER A- D FOR BOTH PARTS, EXPLINATIONS WELCOMED. THANKS!
Step 2: Perform a two-tail hypothesis test ( using the 1-Sample Z option) on columns c1-c50
step 3: place a ' #' after any p-value less than 0.05
From Steps 2 & 3 in Part 1:
A) How many occurrences of p-values less than 0.05 did you have?
B) What Type Error (I or II) do these represent?
C) You were testing the below hypothesis, What is your conclusion when the p-value was less than 0.05?
Ho: Mu = 100
Ha: Mu does not = 100
(Note: Mu = Population Mean)
D) How does your conclusion from Part C above match what you know about where the data came from?
From Steps 4 & 5 in Part 1:
Step 4: Perform a two-tail hypothesis test ( using the 1-Sample Z option) on columns c51-c100.
Step 5: Place a ' $ ' after any p-value greater than or equal to 0.05
A) How many occurrences of p-values greater than or equal to 0.05 did you have?
B) What Type Error (I or II) do these represent?
C) You were testing the below hypothesis, What is your conclusion when the p-value was greater than or equal to 0.05 ?
Ho: Mu = 110
Ha: Mu does not = 110
(Note: Mu = Population Mean)
D) How does your conclusion from Part C above match what you know about where the data came from?
One-Sample Z: C1, C2, C3, C4, C5, C6, C7, C8, C9, C10, ... C48, C49, C50
Descriptive Statistics
Sample N Mean StDev SE Mean 95% CI for
C1 20 96.79 10.36 3.35 (90.22, 103.37)
C2 20 100.70 17.41 3.35 (94.13, 107.28)
C3 20 98.19 16.94 3.35 (91.61, 104.76)
C4 20 101.35 14.64 3.35 (94.77, 107.92)
C5 20 95.16 18.06 3.35 (88.59, 101.73)
C6 20 101.56 17.46 3.35 (94.98, 108.13)
C7 20 103.04 17.82 3.35 (96.46, 109.61)
C8 20 98.02 12.69 3.35 (91.45, 104.60)
C9 20 99.86 14.49 3.35 (93.28, 106.43)
C10 20 99.94 12.29 3.35 (93.37, 106.52)
C11 20 106.88 17.17 3.35 (100.31, 113.46)
C12 20 102.69 13.24 3.35 (96.11, 109.26)
C13 20 96.67 15.57 3.35 (90.10, 103.24)
C14 20 89.00 14.62 3.35 (82.43, 95.58)
C15 20 95.09 12.95 3.35 (88.52, 101.66)
C16 20 97.42 15.85 3.35 (90.84, 103.99)
C17 20 98.18 19.95 3.35 (91.61, 104.75)
C18 20 102.73 12.78 3.35 (96.15, 109.30)
C19 20 97.49 12.79 3.35 (90.92, 104.07)
C20 20 101.46 14.30 3.35 (94.89, 108.04)
C21 20 99.99 18.52 3.35 (93.42, 106.57)
C22 20 99.97 15.69 3.35 (93.39, 106.54)
C23 20 105.06 15.06 3.35 (98.48, 111.63)
C24 20 96.94 15.77 3.35 (90.36, 103.51)
C25 20 111.71 19.13 3.35 (105.13, 118.28)
C26 20 96.93 14.50 3.35 (90.36, 103.50)
C27 20 100.86 12.96 3.35 (94.28, 107.43)
C28 20 103.07 17.02 3.35 (96.50, 109.64)
C29 20 100.32 14.92 3.35 (93.75, 106.89)
C30 20 103.91 14.75 3.35 (97.34, 110.49)
C31 20 99.60 12.80 3.35 (93.03, 106.17)
C32 20 97.66 13.87 3.35 (91.09, 104.23)
C33 20 101.36 9.70 3.35 (94.79, 107.94)
C34 20 95.91 13.83 3.35 (89.34, 102.48)
C35 20 101.62 17.25 3.35 (95.05, 108.19)
C36 20 107.88 13.22 3.35 (101.31, 114.46)
C37 20 98.68 16.73 3.35 (92.10, 105.25)
C38 20 99.74 17.99 3.35 (93.16, 106.31)
C39 20 101.73 14.01 3.35 (95.15, 108.30)
C40 20 96.55 19.70 3.35 (89.97, 103.12)
C41 20 95.07 16.04 3.35 (88.49, 101.64)
C42 20 104.31 16.32 3.35 (97.74, 110.89)
C43 20 105.46 15.27 3.35 (98.88, 112.03)
C44 20 96.56 17.13 3.35 (89.98, 103.13)
C45 20 97.36 10.20 3.35 (90.79, 103.94)
C46 20 99.47 17.02 3.35 (92.90, 106.05)
C47 20 100.96 16.52 3.35 (94.39, 107.53)
C48 20 104.05 15.20 3.35 (97.48, 110.63)
C49 20 98.81 13.85 3.35 (92.23, 105.38)
C50 20 103.92 15.48 3.35 (97.35, 110.50)
: mean of C1, C2, C3, C4, C5, C6, C7, C8, C9, C10, C11, C12, C13, C14, C15, C16, C17, C18,
C19, C20, C21, C22, C23, C24, C25, C26, C27, C28, C29, C30, C31, C32, C33, C34, C35, C36,
C37, C38, C39, C40, C41, C42, C43, C44, C45, C46, C47, C48, C49, C50
Known standard deviation = 15
Test
Null hypothesis H: = 100
Alternative hypothesis H: 100
Sample Z-Value P-Value
C1 -0.96 0.339
C2 0.21 0.834
C3 -0.54 0.589
C4 0.40 0.688
C5 -1.44 0.149
C6 0.46 0.642
C7 0.91 0.365
C8 -0.59 0.555
C9 -0.04 0.966
C10 -0.02 0.987
C11 2.05 0.040
C12 0.80 0.423
C13 -0.99 0.321
C14 -3.28 0.001
C15 -1.46 0.143
C16 -0.77 0.441
C17 -0.54 0.587
C18 0.81 0.417
C19 -0.75 0.455
C20 0.44 0.662
C21 -0.00 0.998
C22 -0.01 0.992
C23 1.51 0.132
C24 -0.91 0.361
C25 3.49 0.000
C26 -0.92 0.360
C27 0.26 0.799
C28 0.92 0.360
C29 0.10 0.924
C30 1.17 0.243
C31 -0.12 0.905
C32 -0.70 0.485
C33 0.41 0.685
C34 -1.22 0.223
C35 0.48 0.629
C36 2.35 0.019
C37 -0.39 0.693
C38 -0.08 0.937
C39 0.51 0.607
C40 -1.03 0.303
C41 -1.47 0.141
C42 1.29 0.198
C43 1.63 0.104
C44 -1.03 0.305
C45 -0.79 0.432
C46 -0.16 0.875
C47 0.29 0.775
C48 1.21 0.227
C49 -0.36 0.722
C50 1.17 0.242
One-Sample Z: C51, C52, C53, C54, C55, C56, C57, C58, ... 8, C99, C100
Descriptive Statistics
Sample N Mean StDev SE Mean 95% CI for
C51 20 100.94 13.24 3.35 (94.37, 107.52)
C52 20 101.30 17.76 3.35 (94.72, 107.87)
C53 20 94.77 12.89 3.35 (88.20, 101.34)
C54 20 102.19 12.75 3.35 (95.61, 108.76)
C55 20 102.59 10.79 3.35 (96.02, 109.17)
C56 20 106.24 14.56 3.35 (99.67, 112.82)
C57 20 97.21 14.09 3.35 (90.64, 103.79)
C58 20 98.88 18.13 3.35 (92.31, 105.46)
C59 20 97.81 12.75 3.35 (91.23, 104.38)
C60 20 101.65 12.97 3.35 (95.07, 108.22)
C61 20 96.74 15.76 3.35 (90.16, 103.31)
C62 20 96.26 14.31 3.35 (89.69, 102.84)
C63 20 97.54 13.38 3.35 (90.96, 104.11)
C64 20 92.33 13.72 3.35 (85.76, 98.91)
C65 20 100.36 14.30 3.35 (93.78, 106.93)
C66 20 102.20 13.58 3.35 (95.63, 108.77)
C67 20 101.77 16.14 3.35 (95.19, 108.34)
C68 20 98.72 16.64 3.35 (92.14, 105.29)
C69 20 105.40 15.18 3.35 (98.82, 111.97)
C70 20 101.54 18.11 3.35 (94.97, 108.11)
C71 20 100.13 13.10 3.35 (93.56, 106.71)
C72 20 98.84 22.92 3.35 (92.27, 105.41)
C73 20 97.19 18.96 3.35 (90.62, 103.77)
C74 20 100.95 15.49 3.35 (94.38, 107.52)
C75 20 101.05 16.52 3.35 (94.48, 107.63)
C76 20 94.13 17.06 3.35 (87.56, 100.71)
C77 20 96.65 15.75 3.35 (90.08, 103.23)
C78 20 98.23 12.48 3.35 (91.65, 104.80)
C79 20 92.92 16.25 3.35 (86.35, 99.50)
C80 20 101.46 15.21 3.35 (94.89, 108.04)
C81 20 101.82 15.10 3.35 (95.25, 108.39)
C82 20 101.71 13.76 3.35 (95.13, 108.28)
C83 20 100.45 9.64 3.35 (93.88, 107.02)
C84 20 100.97 14.96 3.35 (94.40, 107.54)
C85 20 102.22 14.14 3.35 (95.65, 108.80)
C86 20 102.39 18.37 3.35 (95.81, 108.96)
C87 20 102.00 17.85 3.35 (95.43, 108.58)
C88 20 93.64 15.19 3.35 (87.07, 100.22)
C89 20 100.08 15.03 3.35 (93.50, 106.65)
C90 20 96.76 13.38 3.35 (90.19, 103.33)
C91 20 104.80 10.98 3.35 (98.22, 111.37)
C92 20 97.98 15.55 3.35 (91.40, 104.55)
C93 20 100.44 16.10 3.35 (93.87, 107.02)
C94 20 98.30 11.89 3.35 (91.72, 104.87)
C95 20 99.56 17.14 3.35 (92.98, 106.13)
C96 20 99.81 18.17 3.35 (93.23, 106.38)
C97 20 100.98 14.90 3.35 (94.41, 107.55)
C98 20 94.73 14.47 3.35 (88.16, 101.31)
C99 20 100.11 14.74 3.35 (93.54, 106.69)
C100 20 98.55 18.23 3.35 (91.98, 105.13)
: mean of C51, C52, C53, C54, C55, C56, C57, C58, C59, C60, C61, C62, C63, C64, C65, C66,
C67, C68, C69, C70, C71, C72, C73, C74, C75, C76, C77, C78, C79, C80, C81, C82, C83, C84,
C85, C86, C87, C88, C89, C90, C91, C92, C93, C94, C95, C96, C97, C98, C99, C100
Known standard deviation = 15
Test
Null hypothesis H: = 110
Alternative hypothesis H: 110
Sample Z-Value P-Value
C51 -2.70 0.007
C52 -2.60 0.009
C53 -4.54 0.000
C54 -2.33 0.020
C55 -2.21 0.027
C56 -1.12 0.263
C57 -3.81 0.000
C58 -3.31 0.001
C59 -3.63 0.000
C60 -2.49 0.013
C61 -3.95 0.000
C62 -4.10 0.000
C63 -3.72 0.000
C64 -5.27 0.000
C65 -2.87 0.004
C66 -2.33 0.020
C67 -2.45 0.014
C68 -3.36 0.001
C69 -1.37 0.170
C70 -2.52 0.012
C71 -2.94 0.003
C72 -3.33 0.001
C73 -3.82 0.000
C74 -2.70 0.007
C75 -2.67 0.008
C76 -4.73 0.000
C77 -3.98 0.000
C78 -3.51 0.000
C79 -5.09 0.000
C80 -2.54 0.011
C81 -2.44 0.015
C82 -2.47 0.013
C83 -2.85 0.004
C84 -2.69 0.007
C85 -2.32 0.020
C86 -2.27 0.023
C87 -2.38 0.017
C88 -4.88 0.000
C89 -2.96 0.003
C90 -3.95 0.000
C91 -1.55 0.121
C92 -3.58 0.000
C93 -2.85 0.004
C94 -3.49 0.000
C95 -3.11 0.002
C96 -3.04 0.002
C97 -2.69 0.007
C98 -4.55 0.000
C99 -2.95 0.003
C100 -3.41 0.001
Explanation / Answer
For C1-C50 Sample
A) How many occurrences of p-values less than 0.05 did you have?
Ans : In the above sample i.e C1-C50, 4 samples have p-value less than 0.05 namely C11,C14,C25 & C36
B) What Type Error (I or II) do these represent?
Ans. They represent TYPE I error. i.e. Probability of rejecting the null hypothesis when its actually true.
Since the values are less than 0.05 we can reject the null hypothesis and by doing so, we are committing a Type I error by the p-value listed against C11,C14,C25 & C36.
C) You were testing the below hypothesis, What is your conclusion when the p-value was less than 0.05?
Ho: Mu = 100
Ha: Mu does not = 100
(Note: Mu = Population Mean)
Ans. With p-value less than 0.05, we can reject the null hypothesis and accept the alternate hypothesisi..e Mu is equal to 100. In other terms we can state that the sample
D) How does your conclusion from Part C above match what you know about where the data came from?
Ans. Conclusion in part C doesn't match from where the data came from because as part of C) we have said that the mean of the sample is not equal to 100. Whereas the overall sample claim the mean equal to 100.
For Sample C51-100
A) How many occurrences of p-values greater than or equal to 0.05 did you have?
Ans. Sample No. C56,69 and 91 (3 Nos) have p-value greater than or equal to 0.05.
B) What Type Error (I or II) do these represent?
Ans: We are committing a TYPE II error here, because in this case we are failing to reject the null hypothesis(as p-value is greater than 0.05).
C) You were testing the below hypothesis, What is your conclusion when the p-value was greater than or equal to 0.05 ?
Ho: Mu = 110
Ha: Mu does not = 110
(Note: Mu = Population Mean)
Ans: For those sample whose p-value is greater than 0.05 we cannot reject the Null Hypothesis(or accept Alternate Hypothesis) in that case.
Hence, for that samples Mean = 110.
D) How does your conclusion from Part C above match what you know about where the data came from?
Ans: From the above conclusion we can say that the sample is part of the main population data as the Mean of the Population(part of Null Hypothesis), matches with that of Samples under consideration.
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